Reconstruction techniques for cross-sectional imaging are known for deriving information concerning the internal structure of a subject. These reconstruction techniques are derived from mathematical reconstruction algorithms utilizing the fact that sensed data corresponds to a line integral of a function taken through a cross-section of interest. These reconstruction algorithms allocate this function across the cross-section in a process known as convolution back projection.
In computed tomography, a patient or subject cross-section of interest is successively scanned from different directions by an x-radiation source to direct X-rays through the cross-section of interest. One or more detectors positioned on an opposite side of the patient from the source obtain intensity readings of the x-radiation after it has passed through the patients. If enough intensity measurements from different directions are obtained, these intensity readings can be utilized to reconstruct an attenuation image of the patient cross-section.
In nuclear magnetic imaging, a structure is placed within a strong magnetic field to align the magnetic dipoles of atoms within the structure. A gradient field is superimposed at different orientations and the field is pulsed to perturb the magnetic moment of the atoms. As the atoms decay from the perturbed to their aligned state they generate fields characteristic of the structure of the atoms. The gradient field causes the atoms within the structure to decay with different characteristics which can be sorted out by a reconstruction process.
Other uses for reconstruction processing are in geology and astronomy. In geology, for example, the internal structure of the earth can be discerned without actually excavating and physically analyzing the exposed structure.
Various procedures have been tried to improve the accuracy of the information obtained using these reconstruction processes. One calibration technique used to enhance image quality in computed tomography involves the scanning and reconstruction of phantoms. Since the structure of the phantom is known the reconstructed image can be compared with the known structure to establish and determine the cause of discrepancies between the reconstructed image and the known structure.
One problem experienced with computed tomography scanners is an inaccuracy in CT numbers. Reconstruction of water phantoms of varying sizes results in the CT numbers of water being off by as much as 90 CT numbers. The CT numbers of the entire image are shifted up or down by this amount. This inaccuracy seems to be dependent upon the size of the object under examination.
One mathematical equation that solves the computed tomography reconstruction problem takes the form of a spatial domain convolution integral followed by an integration known in the art as back projection. The convolution is carried out directly in a spatial domain by taking the projection data from the X-ray detectors and convolving this data with an appropriate convolution kernel.
This spatial domain convolution, in theory, is carried out over the limits of plus and minus infinity. In the past, however, since it is known that the patient occupies a finite region in space this integration was limited to the specific region of interest occupied by the patient.
Commercial fourth generation computed tomography scanners often use fourier transform techniques rather than spatial domain convolution. According to these more recent procedures a fourier transform of the data is performed, this transformed data is multiplied by a filter function, and then the inverse fourier transform is taken. This solution is documented in the literature. See, for example, "Convolution Reconstruction Techniques for Divergent Beams", Herman et al, Comp Biol Med, Permagon Press 1976, Vol 6, pgs. 259-271. The Herman et al paper is incorporated herein by reference.
The filter function used in scaling the fourier transformed data is the fourier transform of the convolution filter used in spatial calculations. The fourier transform of the convolution filter yields a ramp function which begins at zero and increases linearly with frequency to a maximum value. Since the ramp filter function is based upon a fourier transform of a spatial domain convolution filter used with earlier reconstruction techniques, this filter was not considered as a source for the CT number inaccuracies sometimes experienced in CT imaging.
The present invention solves the mathematical inaccuracies observed in performing image reconstruction in the prior art by use of a new filter function for reconstruction imaging. The new filter is generated by transforming a truncated spatial domain convolution filter at discrete points rather than using a continuous fourier transform of the entire convolution filter.